Freund has been credited with discovering the likes of Erling Haaland, Sadio Mane and Naby Keita and, along with Paris Saint-Germain's Luis Campos, is of interest to the Blues to take over a role new co-owner Todd Boehly took temporary charge of during the summer transfer window.
Ex-Liverpool director Michael Edwards, Monaco’s Paul Mitchell and Brentford technical director Lee Dykes have also been spoken to but Freund and Campos are considered the frontrunners and could both be appointed.
Freund is in England as his Salzburg side on Wednesday night denied new Chelsea boss Graham Potter a win in his first game, and left the door open to joining the manager at Stamford Bridge.
"You should never rule anything out in football and Chelsea are such a huge club," he told Sky Sports Austria. "But I'm sports director in Salzburg and I really enjoy it.
"Chelsea is a huge club in transition. I can't say exactly what will happen in the next few weeks and months."
Freund also confirmed Chelsea's interest in Salzburg striker Benjamin Sesko, who is one of Europe's most sought-after talents.
He added: "I've had exchanges with Chelsea from time to time. We spoke more often a month or two ago because they were interested in Sesko.
"The new owners are interested in how we do it with young players, how we integrate them into the first team. But you do that again and again with other clubs – that's it."